若x+1⼀x=3,则x^3+1⼀x^3的值等于多少

请帮忙写一下详细的步骤,谢谢!
2025-01-06 17:47:26
推荐回答(2个)
回答1:

(x+1/x)^2=x^2+2*x*1/x+1/x^2=2+x^2+1/x^2=3 所以x^2+1/x^2=1
x^3+1/x^3=(x+1/x)(x^2-x*1/x+1/x^2)=3*0=0

回答2:

x+1/x=3
平方
x^2+2+1/x^2=9
x^2+1/x^2=7

x^3+1/x^3=(x+1/x)(x^2-1+1/x^2)=3*(7-1)=18